A199186 - OEIS

%I #8 Feb 07 2025 16:44:05

%S 1,6,3,6,4,4,3,5,5,1,9,5,5,0,4,1,4,2,2,0,6,7,5,9,3,0,3,1,1,8,7,1,2,8,

%T 2,4,5,5,9,3,6,5,4,1,7,1,8,5,9,0,2,6,8,4,2,5,3,3,4,8,5,5,7,2,4,9,6,0,

%U 1,4,7,7,1,1,7,8,8,6,4,9,0,3,3,9,7,9,7,6,2,3,7,9,1,6,2,1,2,7,2

%N Decimal expansion of x<0 satisfying x^2+3*x*cos(x)=3.

%C See A199170 for a guide to related sequences. The Mathematica program includes a graph.

%H <a href="/index/Tra#transcendental">Index entries for transcendental numbers</a>.

%e negative: -1.6364435519550414220675930311871282455...

%e positive:  3.56968633396230393049792896687800143343...

%t a = 1; b = 3; c = 3;

%t f[x_] := a*x^2 + b*x*Cos[x]; g[x_] := c

%t Plot[{f[x], g[x]}, {x, -2 Pi, 2 Pi}, {AxesOrigin -> {0, 0}}]

%t Plot[{f[x], g[x]}, {x, 0, 2}, {AxesOrigin -> {0, 0}}]

%t r = x /. FindRoot[f[x] == g[x], {x, -1.7, -1.6}, WorkingPrecision -> 110]

%t RealDigits[r]  (* A199186 *)

%t r = x /. FindRoot[f[x] == g[x], {x, 3.56, 3.57}, WorkingPrecision -> 110]

%t RealDigits[r]  (*  A199187 *)

%Y Cf. A199170.

%K nonn,cons

%O 1,2

%A _Clark Kimberling_, Nov 04 2011